Technological tools have the potential to offer students the possibility to represent information and relationships embedded in problems and concepts in ways that involve numerical, algebraic, geometric, and visual approaches. In this paper, the authors present and discuss an example in which an initial representation of a mathematical object…

This article explores children's responses to a task that requires them to represent square units in a grid pattern, and highlights the importance to a child's mathematical development of recognizing pattern and structure. The grid task explores children's imagery association with area measurement, and provides clear evidence of students'…

The paper starts from classroom situations about the study of a functional relationship with help of technological tools as a "transposition" of experimental approaches from research mathematical practices. It considers the limitation of this transposition in existing curricula and practices based on the use of non-symbolic software like dynamic…

Following a pretest, 8 participants who were unfamiliar with algebraic and trigonometric functions received a brief presentation on the rectangular coordinate system. Next, they participated in a computer-interactive matching-to-sample procedure that trained formula-to-formula and formula-to-graph relations. Then, they were exposed to 40 novel…

Abstract algebra courses tend to take one of two pedagogical routes: from examples of mathematics structures through definitions to general theorems, or directly from definitions to general theorems. The former route seems to be based on the implicit pedagogical intention that students will use their understanding of particular examples of an…

This study explores pupils' performance and processes in tasks involving equations and inequalities of complex numbers requiring conversions from a geometric representation to an algebraic representation and conversions in the reverse direction, and also in complex numbers problem solving. Data were collected from 95 pupils of the final grade from…

"Cognitive Tutor[R]", a full-year course, covers organizing single variable data, simplifying linear expressions, mathematical modeling, solving systems with linear equations, problem-solving using proportional reasoning, and powers and exponents. Students work at their own pace to develop problem-solving skills. The duration of each…

The State of Florida Department of Education provides pre-and-post-graduation data for public high school graduates throughout Florida. These data were used for the present report to produce data sets for all M-DCPS regular high schools and charter high schools graduating students in 2009 and 2010. Summary data for the district are also provided.…

America's advantage has historically been its people's creativity, flexibility and entrepreneurship. But just as painters need to be proficient in technique and theory to produce great masterpieces, the next generation of Americans will likely require a solid grounding in mathematics and science for their creativity to be maximized in a world…

Purpose: The purpose of this scientific monograph is to show new and creative approaches to different school subjects in primary and secondary level. Methodology: Interdisciplinary and international comparative approaches were used. Now according to the 7th Framework Program, the preferred form of Science Education (www.scientix.eu) is preferred…

Improving teacher effectiveness is high on the list of most education reformers in Colorado, as it is nationally. Effective teaching in the elementary years is of vital importance to ensure not only that children master fundamental skills, but that performance gaps narrow rather than widen beyond repair. Disadvantaged students can catch up…

In a time of evolving Algebraic standards and expectations for Minnesota teachers and students, the establishment of quality professional development and technical assistance can help educators move more confidently toward greater mathematics understanding and, subsequently, successful teaching and learning. To this end, the Minnesota Department…

Today's college ACCUPLACER System's Computerized Placement Test (CPT) plays a major role for determining whether post-secondary students are ready for placement into Arithmetic, Elementary Algebra, Intermediate Algebra, or College Mathematics courses. It is widely used in most college systems in the U.S. This paper discusses some of the issues to…

A yearlong experimental study showed positive effects of a professional development project that involved 19 urban elementary schools, 180 teachers, and 3735 students from one of the lowest performing school districts in California. Algebraic reasoning as generalized arithmetic and the study of relations was used as the centerpiece for work with…

The name of Zoltan P. Dienes (1916- ) stands with those of Jean Piaget, Jerome Bruner, Edward Begle, and Robert Davis as a legendary figure whose work left a lasting impression on the field of mathematics education. Dienes' name is synonymous with the multibase blocks that he invented for the teaching of place value. Among numerous other things,…